# This One To Itself And That One To Itself

Consider all pairs $$(a, b)$$ of natural numbers such that the product $${ a }^{ a }{ b }^{ b }$$, written in base 10, ends in exactly 98 zeroes. If there is only one pair $$(a, b)$$ for which the product $$ab$$ is smallest, then find $$a + b$$.

Note: $$(4, 5)$$ and $$(5, 4)$$ are considered as one pair. Order does not matter.

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